Solving Two Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. It typically involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 3x - 2 < 13?

Back

Add 2 to both sides: 3x < 15. Then divide by 3: x < 5.

Front

What is the solution to the inequality 7b - 3 < 11?

Back

Add 3 to both sides: 7b < 14. Then divide by 7: b < 2.

Front

How do you solve the inequality 2x + 6 > 12?

Back

Subtract 6 from both sides: 2x > 6. Then divide by 2: x > 3.

Front

What does the inequality 6(n + 2) < -72 represent?

Back

Distribute 6: 6n + 12 < -72. Then subtract 12: 6n < -84. Finally, divide by 6: n < -14.

Front

What is the solution to the inequality -2(x + 2) < 14?

Back

Distribute -2: -2x - 4 < 14. Add 4 to both sides: -2x < 18. Then divide by -2 (remember to flip the inequality): x > -9.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Front

What is the difference between a solution to an equation and a solution to an inequality?

Back

A solution to an equation is a specific value that makes the equation true, while a solution to an inequality represents a range of values that satisfy the inequality.

Front

What is the graphical representation of an inequality?

Back

The graphical representation of an inequality is shown on a number line, where a closed dot indicates a value is included (≤ or ≥) and an open dot indicates it is not included (< or >).

Front

How do you check if a value is a solution to an inequality?

Back

Substitute the value into the inequality and see if the statement is true.